Comparison of powers for the sphericity tests using both the asymptotic distribution and the bootstrap

The asymptotic distributions of two tests for sphericity:the locally most powerful invariant test and the likelihood ratio test are derived under the general alternaties ∑?σ² I. The powers of these two tests are then compared when the data are from a trivariate normal population. The bootstrap method is also used to obtain the powers and the powers obtained by this method agree with those from the asymptotic distributions.